Related papers: A Guided Tour to Normalized Volume
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of so doing, a natural regularization of the vertices is suggested. The regularized vertices…
Abandoning dimensional regularization allows important simplifications in loop calculations and gives a handle to interpret non-renormalizable Quantum Field Theories. I review the current status of FDR, a fully four-dimensional approach to…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…
Motivated by problems of uncertainty propagation and robust estimation we are interested in computing a polynomial sublevel set of fixed degree and minimum volume that contains a given semialgebraic set K. At this level of generality this…
We reveal that a fundamental minimal length naturally replaces the Schwarzschild singularity with future infinity, formalizing the ``asymptotic throat'' as a geometric inevitability. This scheme avoids the topology changes, multiple…
We study the regularization ambiguities in an exact renormalized (1+1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation…
We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various…
We discuss some aspects of recent research as well as more general issues about motivation, useful methods and open problems in the field of cosmological singularities. In particular, we review some of the approaches to the general area and…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
I review the recent efforts in the search for a minimal and predictive nonsupersymmetric SO(10) Grand Unified Thoery (GUT). The outcome is the revival of a minimal scenario in which a long standing result, claiming the incompatibility…
There is rich literature on regular black holes from loop quantum gravity (LQG), where quantum geometry effects resolve the singularity, leading to a quantum extension of the classical space-time. As we will see, the mechanism that resolves…
This article employs techniques from convex analysis to present characterizations of (maximal) $n-$monotonicity, similar to the well-established characterizations of (maximal) monotonicity found in the existing literature. These…
For finite volume field theories with discrete translational invariance, conserved currents can be additively renormalized by infrared effects. We demonstrate this for pions using chiral perturbation theory coupled to electromagnetism in a…
Quantum cosmology may restrict the class of gauge models which unify electroweak and strong interactions. In particular, if one studies the normalizability criterion for the one-loop wave function of the universe in a de Sitter background…
We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
The long story of the oscillatory approach to the initial cosmological singularity and its more recent incarnation in multidimensional universe models is told.